Blockchain-enforced resource budgets for adaptive wildfire monitoring agents can be modeled as a physics-constrained energy minimization problem, where agent compute allocations (Resourced Authority) emulate spring-damper dynamics (Formation Matrix) to prevent coordination collapse under high-risk conditions.

Under a multi-agent wildfire monitoring system in which each agent's compute/communication budget is allocated and enforced via on-chain smart-contract rules, the time-evolution of aggregate agent coordination error e(t) (deviation from target sensing-coverage formation) can be fit by a second-order spring-damper ODE: m·e''(t) + c·e'(t) + k·e(t) = F_risk(t), where k (spring/formation constant) and c (damping constant) are derived from the blockchain budget-allocation policy (Resourced Authority) rather than free-fit parameters. The hypothesis is falsifiable: it predicts that (a) a physics-constrained budget policy (chosen so the implied (k,c) keep the system in the critically-damped-to-overdamped regime, i.e. damping ratio ζ = c / (2√(mk)) ≥ 0.8) will keep coordination error bounded (no divergence, no oscillatory collapse) under simulated high-risk fire-spread scenarios with resource scarcity, whereas (b) an unconstrained or naively-throttled baseline budget policy (ζ < 0.3 or undefined) will exhibit measurable coordination collapse (error growth >3x baseline steady-state or agent desynchronization events) under matched scarcity conditions, at statistically significant rates (p<0.05, n≥30 runs per condition).

Minimum viable test: simulate N=20 agents in a 2D grid environment with a stochastic fire-spread model (cellular automaton, calibrated to Rothermel-like spread rates) driving a time-varying risk field. Compare 3 conditions: (1) Physics-Constrained Budget (PCB) — blockchain-simulated smart contract sets per-agent compute/comm budget mapped to (k,c) targeting ζ≥0.8; (2) Naive Fixed Budget (NFB) — static equal budget allocation, no dynamic feedback; (3) Unconstrained (UNC) — no budget enforcement (oracle/ideal compute). Run 30 Monte Carlo trials per condition per scenario, across 3 fire-spread topologies (single-front, multi-front, wind-driven erratic) and 2 scarcity levels (mild: 70% nominal compute available; severe: 30% nominal). Measure coordination error trajectory, fit ODE parameters via least-squares/Kalman filter, and test collapse-rate differences via chi-squared/logistic regression.

# Pseudocode overview

class BudgetContract:
    def allocate(agent_id, risk_level, ledger_state):
        # monotonic mapping: more risk + more ledger credit -> higher k (stiffer pull to formation)
        # scarcity -> lower overall budget -> scales both k and c down proportionally
        k = base_k * f(ledger_state.credits, risk_level)
        c = 2 * zeta_target * sqrt(mass * k)
        return ComputeBudget(k=k, c=c, compute_units=...)

class Agent:
    def update(self, dt, risk_field, budget):
        error = self.position - self.target_formation_position(risk_field)
        accel = (-budget.k * error - budget.c * self.velocity + F_risk(risk_field)) / mass
        self.velocity += accel * dt
        self.position += self.velocity * dt

class FireSpreadCA:
    def step(self):
        # cellular automaton spread update
        ...

# Main loop
for trial in range(30):
    for topology in [single_front, multi_front, wind_driven]:
        for scarcity in [0.7, 0.3]:
            for arm in [PCB, NFB, UNC]:
                env = init_env(topology, scarcity, arm)
                for t in range(500):
                    risk_field = env.fire.step()
                    for agent in env.agents:
                        budget = contract.allocate(agent.id, risk_field.local_risk(agent), ledger)
                        agent.update(dt, risk_field, budget)
                    log(env.coordination_error())
                fit_ode(log_trajectory)
                record_collapse(log_trajectory)